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184_notes:examples:week12_force_between_wires [2017/11/12 17:08] – dmcpadden | 184_notes:examples:week12_force_between_wires [2018/07/19 13:32] – curdemma | ||
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===== Magnetic Force between Two Current-Carrying Wires ===== | ===== Magnetic Force between Two Current-Carrying Wires ===== | ||
Two parallel wires have currents in opposite directions, $I_1$ and $I_2$. They are situated a distance $R$ from one another. What is the force per length $L$ of one wire on the other? | Two parallel wires have currents in opposite directions, $I_1$ and $I_2$. They are situated a distance $R$ from one another. What is the force per length $L$ of one wire on the other? | ||
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* We represent the situation with diagram below. | * We represent the situation with diagram below. | ||
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====Solution==== | ====Solution==== | ||
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If we wanted to write the force per length (rather than the total force), we would simply divide by L on both sides: | If we wanted to write the force per length (rather than the total force), we would simply divide by L on both sides: | ||
$$\frac{\vec{F}_{1 \rightarrow 2}}{L} | $$\frac{\vec{F}_{1 \rightarrow 2}}{L} | ||
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If instead we wanted to find the force per length on Wire 1 from Wire 2, then we could do this whole process over again (find the magnetic field from Wire 2 at the location of Wire 1, find $d\vec{l}_1$, | If instead we wanted to find the force per length on Wire 1 from Wire 2, then we could do this whole process over again (find the magnetic field from Wire 2 at the location of Wire 1, find $d\vec{l}_1$, |